for every \(x\in M\)  whenever they exist (see [1]}). We refer to \(u_M^+\)  and \(u_M^-\)  as the two-sided traces of \(u\)  at \(M\)  and we notice that they are uniquely determined up to a permutation when changing the sign of \(\nu _M.\) 
If \(U=\mathrm {Int}(A)\)  for some measurable set \(A\)  with \(\mathcal {H}^1(\partial A)<+\infty \)  and \(M:=\partial ^r A\) , we use the simplified notations \(u_{\partial A}^\pm \)  on \(A^{(1)}\cap \partial ^r A,\)  and \({\rm tr}_Au:=u_{\partial A}^+\)  on \(\partial ^* A,\)  where on \(\partial ^*A\)  we always choose \(\nu _M\)  in (REF ) as the generalized outer unit normal to \(A.\)  Moreover, we define
\(S_u^A:=\lbrace x\in A^{(1)}\cap \partial ^r A:\, u_{\partial A}^+(x) \ne u_{\partial A}^-(x)\rbrace .\) 
